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WA573

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These are questions asked by WA573

How to draw phase portrait of an ODE?...

WA573 80 Maple 2020
ode differential-equations phaseportrait
October 09 2022
1 2

How to draw a phase portrait of (2) same as in the attached figure? I tried it by using dsolve, but couldn't redraw it.  

> 

restart
> 

with(DEtools); with(plots)
> 

alias(phi = phi(xi))

phi

 (1)
> 

eq := (1/2)*m*(diff(phi, xi))^2+`Φ__∓` = h

(1/2)*m*(diff(phi, xi))^2+`Φ__∓` = h

 (2)
> 

NULL
> 

`Φ__∓` = `&-+`(1-cos(phi))

`Φ__∓` = `&-+`(1-cos(phi))

 (3)

``

Download PP.mw

How to integrate this equation?...

WA573 80 Maple 2020
integration ode differential-equations
October 05 2022
1 0

Is it possible to integrate eq (1) in such a way that the final result will be of 1st order differential equation? 

 


 

> 

restart
> 

with(PDEtools)
> 

eq := (diff(U(z), z))^3*(diff(U(z), z, z))+(diff(U(z), z))*(diff(U(z), z, z, z, z))-(diff(U(z), z, z))*(diff(U(z), z, z, z)) = 0

(diff(U(z), z))^3*(diff(diff(U(z), z), z))+(diff(U(z), z))*(diff(diff(diff(diff(U(z), z), z), z), z))-(diff(diff(U(z), z), z))*(diff(diff(diff(U(z), z), z), z)) = 0

 (1)
> 

eq1 := map(convert, eq, diff); eq2 := map(int, lhs(eq1), z)-C1 = 0

(diff(U(z), z))^3*(diff(diff(U(z), z), z))+(diff(U(z), z))*(diff(diff(diff(diff(U(z), z), z), z), z))-(diff(diff(U(z), z), z))*(diff(diff(diff(U(z), z), z), z)) = 0

  

(1/4)*(diff(U(z), z))^4-(diff(diff(U(z), z), z))^2+(diff(diff(diff(U(z), z), z), z))*(diff(U(z), z))-C1 = 0

 (2)

``


 

Download inttegration.mw

how to collect the terms of like powers ...

WA573 80 Maple 2020
algebraic coefficients
September 28 2022
1 4

After substitution of (10) into (4), how to collect the terms of like powers of eta (i.e., eta^-3, eta^-2,eta^-1, eta^0, eta^1,eta^2 ), and equate the coefficients to
zero, get a system of algebraic equations for A[m]?

 

PA.mw 

How to find values of w?...

WA573 80 Maple 18
eigenvalues determinant
September 22 2022
2 2

How to find values of w for which determinant of A is zero?

determinant.mw

Can we convert expression into determina...

WA573 80 Maple 18
linear-algebra determinant
August 30 2022
1 0

Can we convert expression into determinant of 3 rows and 3 columns?

convert.mw

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